Practice Questions

Q62.Let z = 5 5 + . If R(z) and I(z) respectively denote the real and imaginary parts of z, ( √32 + 2i ) ( √32 −i2 ) then (1) I(z) = 0 (2) R(z) < 0 and I(z) > 0 (3) R(z) > 0 and I(z) > 0 (4) R(z) = −3

Q62.Let z ∈C with Im(z) = 10 and it satisfies 22 z+nz−n = 2i −1 for some natural number n. Then (1) n = 20 and Re(z) = 10 (2) n = 40 and Re(z) = 10 (3) n = 20 and Re(z) = −10 (4) n = 40 and Re(z) = −10

Q62.If z z α (α ∈R) is a purely imaginary number and |z| = 2, then a value of α is : + (1) 1 (2) 12 (3) √2 (4) 2

Q62.If a > 0 and z = (1+i)2a−i √25 (1) −15 −35 i (2) −35 −15 i (3) 1 5 −35 i (4) −15 + 53 i

Q62.Let z be a complex number such that |z| + z = 3 + i ( where i = √−1) Then |z| is equal to : (1) √34 (2) 5 3 3 (3) √41 (4) 5 4 4

Q62.Let z1 and z2 be any two non-zero complex numbers such that 3|z1| = 4|z2|. If z = 3z1 + 2z2 then maximum 2z2 3z1 value of |z| is Note: In actual paper value of |z| was asked. Hence, none of the options given were correct. So we have modified the question as well as options. (1) 7 (2) 9 2 2 (3) 5 (4) 1 2 2 √172

Q62.Let (−2 −13 i) 3 = x+iy27 (i = √−1), (1) 91 (2) -85 (3) 85 (4) -91

Q62.All the points in the set S = { α+iα−i , α ∈R}, i = √−1 lie on a (1) straight line whose slope is −1 (2) circle whose radius is √2 (3) circle whose radius is 1 (4) straight line whose slope is 1 JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper

Q62.Let 𝐴= 𝜃∈- 𝜋 𝜋: 3 + 2𝑖 sin𝜃 is purely imaginary . Then the sum of the elements in 𝐴 is: 2, 1 - 2𝑖 sin𝜃 5𝜋 (1) (2) π 6 (3) 2𝜋 (4) 3𝜋 3 4

Q62.The equation |𝑧- 𝑖| = | 𝑧- 1 | , 𝑖= √-1, represents: 1 (1) a circle of radius (2) a circle of radius 1 2 (3) the line through the origin with slope 1 (4) the line through the origin with slope -1 JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q63.There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is : (1) 11 (2) 12 (3) 7 (4) 9 is equal to 225K,

Q63.If ∑25r=0{(50Cr)(50−rC25−r)} = K(50C25) , then K is equal to (1) 225 (2) 225 −1 (3) 224 (4) (25)2 is 720, is

Q63.The number of 6 digit number that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is: (1) 36 (2) 60 (3) 72 (4) 48

Q63.If 19 th term of a non-zero A.P. is zero, then its (49th term): (29th term) is: (1) 4: 1 (2) 1: 3 (3) 3: 1 (4) 2: 1 2 n where q is a real number + + … +

Q63.If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r can not be equal to: (1) 3 (2) 3 4 2 (3) 5 (4) 7 4 4

Q63.A committee of 11 member is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then: (1) m = n = 68 (2) n = m –8 (3) m = n = 78 (4) m + n = 68 A is

Q63.The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 + … upto 11th term is: (1) 945 (2) 916 (3) 946 (4) 915

Q63.The Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is: (1) 220 (2) 221 (3) 220 + 1 (4) 220 - 1

Q63.Let S = {1, 2, 3, … . , 100}, then number of non-empty subsets A of S such that the product of elements in A is even is : (1) 2100 −1 (2) 250 + 1 (3) 250(250 −1) (4) 250 −1

Q63.A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to (1) 24 (2) 27 (3) 25 (4) 28

Q63.All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is (1) 175 (2) 162 (3) 180 (4) 160

Q63.Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys 𝐴 and 𝐵, who refuse to be the members of the same JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper team, is: (1) 300 (2) 200 (3) 500 (4) 350

Q63.If 𝑧= √3 + 𝑖= √-1, then 1 + 𝑖𝑧+ 𝑧5 + 𝑖𝑧89 is equal to: 2 2 (1) -1 (2) 1 (3) 0 (4) -1 + 2𝑖9

Q63.Let z0 be a root of quadratic equation, x2 + x + 1 = 0. If z = 3 + 6iz810 −3iz930 , then arg (z) is equal to: (1) 0 (2) π4 (3) π (4) π 6 3

Q63.Suppose that 20 pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is: (1) 170 (2) 180 (3) 210 (4) 190